Brill-Noether theory is a classical subject that studies parameter spaces of linear series on an algebraic curve X (i.e. essentially maps to projective space). Prym-Brill-Noether theory ask for the natural analogue of Brill-Noether theory in the case that X has symmetries, e.g. in the presence of a fixed point free involution. In this case we consider natural Brill-Noether-loci in the corresponding Prym variety and study its geometric properties. In this talk I will outline a new approach to this story using methods from tropical geometry. This turns out to naturally lead to the study of tropicalizations of strata of abelian differentials and, in particular, our recent solution of the realizability problem for effective tropical canonical divisors.

This talk is based on joint work with Y. Len as well as M. Möller and A. Werner (as well as work in progress with D. Ranganathan and J. Wise).

Zoom: https://washington.zoom.